So which is it going to be: the thick white coaxial cable coiled up behind your television set? Or the thin plastic phone cord behind your desk?

The two wires that connect into the most American homes are in competition to give you local and long-distance phone service, high-speed Internet access and hundreds of channels of video -- all on a single monthly bill.

The vision of a "one-wire world" has kept investors, regulators and the industry itself puzzling for years. When Congress passed the broad Telecommunications Act of 1996, changing the country's system of regulation overnight, it envisioned just such a system.

But so far we haven't seen it. Cable TV operators have shunned the phone business. Phone companies have tried and abandoned ways to deliver television over their lines. And only recently has each industry become serious about upgrading its networks for high-speed Internet access.

This past week AT&T Corp. put the one-wire idea back in vogue. By announcing it would acquire cable giant Tele-Communications Inc. for $48 billion in stock and debt, the nation's largest phone company did the unthinkable. It cast a vote for the much-maligned cable industry as AT&T's preferred route to offering one-stop shopping for all communications needs.

With that move AT&T is parting ways with its telephone industry brethren. "Phone networks already are completely connected," Bell Atlantic Corp. spokesman Eric Rabe said. Cable companies "aren't hooked together like you have to be to offer phone service."

Once upon a time the single-wire vision was called "fiber to the home." A single strand of high-capacity fiber-optic cable connected to houses and apartments would carry movies, phone calls and data services. But when stringing fiber to more than 100 million homes proved expensive, the industry began looking at ways to soup up the existing connections: phone and cable TV lines.

Each has advantages and drawbacks. Cable TV wires have very high capacity and can be upgraded with comparative ease to carry ultra high-speed Internet service along with the TV shows into homes. But they can't readily send information the other way -- out of the house.

Phone lines, on the other hand, are fully two-way, but have very limited "bandwidth," as engineers call data capacity. Forcing a movie through them takes great feats of engineering.

Here and there, the industry relies on a third route into the home: the satellite dish. Bell Atlantic is beginning to market the DirecTV pay television service under its brand name. But dishes have drawbacks too. As designed, they are one-way devices -- incoming to the house -- requiring use of a phone line for communications out of the house.

The rise of the Internet has given the cable and phone industries a common goal: Each is striving to transform its system into what are in essence huge computer networks that can send voice, data and graphics as efficient electronic "packets" of information, an approach known as Internet Protocol, or IP.

Long-distance telephone company Sprint Corp. recently drew major publicity with a plan to build a coast-to-coast IP network that it promises would carry video, Internet and other services cheaply and reliably.

That service would rely on local phone companies upgrading their networks to carry the service for "the final mile" into the home. AT&T, however, is betting that upgrading TCI's cable networks for two-way IP communications is preferable to relying on local phone companies to build higher-capacity links into homes.

"We look not to what the cable system is, but to what it can become," said AT&T President John Zeglis, who will run AT&T's newly created cable-phone company.

It will cost AT&T billions to achieve its goals. TCI's current plan to spend $1.8 billion to upgrade its networks to two-way Internet services hadn't included telephone services. AT&T estimates it will cost another $400 to $500 a customer to bring phone service over cable, in addition to TCI's upgrade costs.

TCI President Leo Hindery said the entire TCI network will be two-way ready by mid-2000, and that adding voice services was only an "incremental" step once the IP network is completed. Telephone service will be ready in 12 to 18 months, he said.

There is wide skepticism in the industry as to whether the AT&T-TCI partnership can pull it off. Both companies have suffered falling stock prices since the deal was announced, as investors sold off shares.

"It appears to be a very rich price to solve the local [phone] problem," Sprint Chairman William Esrey said.

Jim Wahl of the Yankee Group market research firm in Boston said: "I'm confident they can do it. I'm just not as confident about their timing."

Even if they do succeed, AT&T's problems of access to homes won't be over: TCI and all of its affiliates together go into only a third of the nation's homes. AT&T recently bought local service provider Teleport and is pursuing what it calls Project Angel, a way to offer broadband services into the home using fixed radio towers, but that remains an uncertain technology that will be much more expensive.

But in the telecom business of the late 1990s, few things are too expensive if they hold out a chance to win the race for one wire.

Cable or Phone?

Cable and phone industries are trying to transform themselves into comprehensive systems providing Internet access, local and long-distance phone, video and cable services. But both face considerable technological hurdles as they try to send more information through their lines.

Here are the basics of the lines into the home used for phone and cable:

Coaxial cable TV line

Made of copper, has very high capacity, capable of carrying numerous video signals at once for short distances.

Typically used in one-way transmission of video from cable TV company to subscribers' homes. Can be modified to provide two-way transmission.

Copper wire phone line

Designed for human voices decades ago, it transmits a narrow range of frequencies via electrical signals. Can be "noisy" for data transmission because splices in the wire can distort transmissions and the resulting corrections that must be sent take up capacity.

Can carry analog or digital signals, depending on the electronics sending the transmission.